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Math Help - Combining 2 Functions

  1. #1
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    Combining 2 Functions

    Hi, can someone help me with this question:

    The fuction P(t) = 5000-1000cos((pi/6)t) models the deer population in a provincial park. A disease in the deer population has caused it to decline. Biologists have discovered that the deer population is decreasing by 25 deer each month.

    a) Assuming that this pattern continues, determine the new function that will model the deer population over time and discuss its characteristics
    b) estimate when the deer population in this park will be extinct

    a) For a, i know that the new equation is f(t) = 5000-25t-1000cos((pi/6)t) but I'm not sure how to graph it to figure out it's characteristics. Is it even possible to graph by hand? Or is graphing software needed?

    b) For b I'm not sure how to figure this out at all. I start off making the f(t) equation equal to zero but the cos throws me off. Can someone please show me a step by step process of what I'm suppose to do? Or is this question only possible using graphing software as well?

    Thanks a lot.
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  2. #2
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    I'm going to try to tackle this problem but I need you to clarify the notation of the provided equation.

    The deer population is equal to 5000 minus 1000 times the cosine of Pi (3.14 ....) divided by 6 times 't'

    is that right?

    Also, what unit is 't' given in? Years? Months?
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  3. #3
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    Quote Originally Posted by Masterthief1324 View Post
    I'm going to try to tackle this problem but I need you to clarify the notation of the provided equation.

    The deer population is equal to 5000 minus 1000 times the cosine of Pi (3.14 ....) divided by 6 times 't'

    is that right?

    Also, what unit is 't' given in? Years? Months?
    Yes, that's the correct notation. T is given in months after January.

    Thanks!
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